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The description for this book, Linear Inequalities and Related Systems. (AM-38), Volume 38, will be forthcoming.
Operational research. Game theory --- Linear programming. --- Matrices. --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Production scheduling --- Programming (Mathematics) --- Banach space. --- Basic solution (linear programming). --- Big O notation. --- Bilinear form. --- Boundary (topology). --- Brouwer fixed-point theorem. --- Characterization (mathematics). --- Coefficient. --- Combination. --- Computation. --- Computational problem. --- Convex combination. --- Convex cone. --- Convex hull. --- Convex set. --- Corollary. --- Correlation and dependence. --- Cramer's rule. --- Cyclic permutation. --- Dedekind cut. --- Degeneracy (mathematics). --- Determinant. --- Diagram (category theory). --- Dilworth's theorem. --- Dimension (vector space). --- Directional derivative. --- Disjoint sets. --- Doubly stochastic matrix. --- Dual space. --- Duality (mathematics). --- Duality (optimization). --- Eigenvalues and eigenvectors. --- Elementary proof. --- Equation solving. --- Equation. --- Equivalence class. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- Extreme point. --- Fixed-point theorem. --- Functional analysis. --- Fundamental theorem. --- General equilibrium theory. --- Hall's theorem. --- Hilbert space. --- Incidence matrix. --- Inequality (mathematics). --- Infimum and supremum. --- Invertible matrix. --- Kakutani fixed-point theorem. --- Lagrange multiplier. --- Linear equation. --- Linear inequality. --- Linear map. --- Linear space (geometry). --- Linear subspace. --- Loss function. --- Main diagonal. --- Mathematical induction. --- Mathematical optimization. --- Mathematical problem. --- Max-flow min-cut theorem. --- Maxima and minima. --- Maximal set. --- Maximum flow problem. --- Menger's theorem. --- Minor (linear algebra). --- Monotonic function. --- N-vector. --- Nonlinear programming. --- Nonnegative matrix. --- Parity (mathematics). --- Partially ordered set. --- Permutation matrix. --- Permutation. --- Polyhedron. --- Quantity. --- Representation theorem. --- Row and column vectors. --- Scientific notation. --- Sensitivity analysis. --- Set notation. --- Sign (mathematics). --- Simplex algorithm. --- Simultaneous equations. --- Solution set. --- Special case. --- Subset. --- Summation. --- System of linear equations. --- Theorem. --- Transpose. --- Unit sphere. --- Unit vector. --- Upper and lower bounds. --- Variable (mathematics). --- Vector space. --- Von Neumann's theorem.
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This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and it analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation. The unifying theme is a formal model for robotic networks that explicitly incorporates their communication, sensing, control, and processing capabilities--a model that in turn leads to a common formal language to describe and analyze coordination algorithms. Written for first- and second-year graduate students in control and robotics, the book will also be useful to researchers in control theory, robotics, distributed algorithms, and automata theory. The book provides explanations of the basic concepts and main results, as well as numerous examples and exercises. Self-contained exposition of graph-theoretic concepts, distributed algorithms, and complexity measures for processor networks with fixed interconnection topology and for robotic networks with position-dependent interconnection topology Detailed treatment of averaging and consensus algorithms interpreted as linear iterations on synchronous networks Introduction of geometric notions such as partitions, proximity graphs, and multicenter functions Detailed treatment of motion coordination algorithms for deployment, rendezvous, connectivity maintenance, and boundary estimation
Robotics. --- Computer algorithms. --- Robots --- Automation --- Machine theory --- Robot control --- Robotics --- Algorithms --- Control systems. --- Computer algorithms --- Control systems --- 1-center problem. --- Adjacency matrix. --- Aggregate function. --- Algebraic connectivity. --- Algebraic topology (object). --- Algorithm. --- Analysis of algorithms. --- Approximation algorithm. --- Asynchronous system. --- Bellman–Ford algorithm. --- Bifurcation theory. --- Bounded set (topological vector space). --- Calculation. --- Cartesian product. --- Centroid. --- Chebyshev center. --- Circulant matrix. --- Circumscribed circle. --- Cluster analysis. --- Combinatorial optimization. --- Combinatorics. --- Communication complexity. --- Computation. --- Computational complexity theory. --- Computational geometry. --- Computational model. --- Computer simulation. --- Computer vision. --- Connected component (graph theory). --- Connectivity (graph theory). --- Consensus (computer science). --- Control function (econometrics). --- Differentiable function. --- Dijkstra's algorithm. --- Dimensional analysis. --- Directed acyclic graph. --- Directed graph. --- Discrete time and continuous time. --- Disk (mathematics). --- Distributed algorithm. --- Doubly stochastic matrix. --- Dynamical system. --- Eigenvalues and eigenvectors. --- Estimation. --- Euclidean space. --- Function composition. --- Hybrid system. --- Information theory. --- Initial condition. --- Instance (computer science). --- Invariance principle (linguistics). --- Invertible matrix. --- Iteration. --- Iterative method. --- Kinematics. --- Laplacian matrix. --- Leader election. --- Linear dynamical system. --- Linear interpolation. --- Linear programming. --- Lipschitz continuity. --- Lyapunov function. --- Markov chain. --- Mathematical induction. --- Mathematical optimization. --- Mobile robot. --- Motion planning. --- Multi-agent system. --- Network model. --- Network topology. --- Norm (mathematics). --- Numerical integration. --- Optimal control. --- Optimization problem. --- Parameter (computer programming). --- Partition of a set. --- Percolation theory. --- Permutation matrix. --- Polytope. --- Proportionality (mathematics). --- Quantifier (logic). --- Quantization (signal processing). --- Robustness (computer science). --- Scientific notation. --- Sensor. --- Set (mathematics). --- Simply connected space. --- Simulation. --- Simultaneous equations. --- State space. --- State variable. --- Stochastic matrix. --- Stochastic. --- Strongly connected component. --- Synchronous network. --- Theorem. --- Time complexity. --- Topology. --- Variable (mathematics). --- Vector field.
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